The regularity of Euclidean Lipschitz boundaries with prescribed mean curvature in three-dimensional contact sub-Riemannian manifolds

Abstract

In this paper we consider a set $E\subsetΩ$ with prescribed mean curvature $f\in C(Ω)$ and Euclidean Lipschitz boundary $\partial E=Σ$ inside a three-dimensional contact sub-Riemannian manifold $M$. We prove that if $Σ$ is locally a regular intrinsic graph, the characteristic curves are of class $C^2$. The result is shape and improves the ones contained in \cite{MR2583494} and \cite{GalRit15}.

11 pages. Final version to appears in Nonlinear Analysis Series A: Theory, Methods & Applications